2 Mean field theory

In this chapter, we explore the mean field theory of two physical systems —

binary fluids and nematic liquid crystals. In mean field theory, what we do is we

write down the free energy of the system, and then find a state

φ

that minimizes

the free energy. By the Boltzmann distribution, this would be the “most likely

state” of the system, and we can pretend F

TOT

= F [φ].

This is actually not a very robust system, since it ignores all the fluctuations

about the minimum, but gives a good starting point for understanding the

system.